Advertisements
Advertisements
Question
Solve the following differential equation:
`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`
Advertisements
Solution
The equation can be written as
`tan y ("d"y)/("d"x)` = cos(x + y) + cos(x – y)
W.K.T cos(A + B) + cos(A – B) = 2 cos A cos B
Here A = x, B = y
∴ `tan y ("d"y)/("d"x)` = 2 cos x cos y
`tany/cosy` dy = 2 cos x dx
Taking integration on both sides, we get
`int tany/cosy "d"y = 2int cos x "d"x`
`2 int tan y sec y "d"y = 2 int c x "d"x`
sec y = 2 sin x + C
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
`y"d"x + (1 + x^2)tan^-1x "d"y`= 0
Solve the following differential equation:
`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`
Solve the following differential equation:
`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Choose the correct alternative:
The general solution of the differential equation `log(("d"y)/("d"x)) = x + y` is
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`
Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0
Solve: ydx – xdy = 0 dy
Solve: `("d"y)/("d"x) = y sin 2x`
Solve the following:
`("d"y)/("d"x) + y tan x = cos^3x`
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
The differential equation of y = mx + c is (m and c are arbitrary constants)
Choose the correct alternative:
The differential equation of x2 + y2 = a2
Choose the correct alternative:
Which of the following is the homogeneous differential equation?
Form the differential equation having for its general solution y = ax2 + bx
Solve (x2 + y2) dx + 2xy dy = 0
Solve (D2 – 3D + 2)y = e4x given y = 0 when x = 0 and x = 1
Solve `("d"y)/("d"x) = xy + x + y + 1`
